用有限Hankel变换就常见的环形分布激光束情形,推导得到了激光束辐照透过窗口镜引起热传导温度场和热变形分布的理论解,以此计算结果与实验值相比较,分析了白宝石、石英两种窗口镜在激光辐照下的热变形情况.分析结果表明,在激光束辐照的4s时段内,温升场主要集中在激光束辐照的环形区内,在镜面内远未拉平,由此引起的厚度方向热膨胀变形也很不均匀.材料对激光的吸收系数和热膨胀系数以及热扩散率分别是决定热变形量值大小和空间分布的最主要的物性参数.

By employing the limited Hankel integral transform, heat conduction and thermal deformation of optical windows induced by annularly-distributed laser beam are theoretically studied. The temperature increment and thermal deformation fields are expressed as infinite series. Then the theoretical results for sapphire and fused silica optical windows are calculated and compared with those from experiments. It is found that in 4 s of irradiation, remarkable temperature rise occurs mainly in the irradiated annular area while its distribution over the whole window is far from a uniform one, so does the thermal deformation. Among all the parameters of materials', the absorption coefficient to incident laser and thermal expansion coefficient, and thermal diffusion coefficient are of the most importance in determining magnitude and distribution characteristics of the window thermal deformation field, respectively.